In my reading I came across the word siddha and nitya siddha. By now I should know what this word means, but still…I wanted some clarification. So I went to Vani Quotes and did a search. One of the best definitions I could find came from the following letter to Mukunda dasa:

…Your next question, whether the Spiritual Master was formerly a conditioned soul, actually a bona fide Spiritual Master is never a conditioned soul. There are three kinds of liberated persons. They are called 1) sadhan siddha, 2) kripa siddha, and 3) nitya siddha. Sadhan siddha means one who has attained perfection by executing the regulative principles of devotional service. Kripa siddha means one who has attained perfection by the special mercy of Krishna and the Spiritual Master, and nitya siddha means one who was never contaminated. The symptoms of nitya siddha is that from the beginning of his life he is attached to Krishna, and he is never tired of rendering service to Krishna. So we have to know what is what by these symptoms. But when one is actually on the siddha platform there is no such distinction as to who is sadhan, kripa, or nitya siddha. When one is siddha, there is no distinction what is what. Just like when the river water glides down to the Atlantic Ocean nobody can distinguish which portion was the Hudson River or some other river. Neither is there any necessity to make any such distinction. Actually, every living entity is eternally uncontaminated, although he may be in the material touch. This is the version of the Vedas. Asanga ayam purusha—the living entity is uncontaminated. Just like when there is a drop of oil in water you can immediately distinguish the oil from the water, and the water never mixes with the oil. Similarly, a living entity, although in material contact, is always distinct from the matter.

This was an amazing answer. For more on the meaning of nitya siddha

Srimad-Bhagavatam

Mahā-bhāgavatas are called nitya-siddhas, or souls liberated from birth.
(SB 2.3.15, Purport)

According to Śrīdhara Svāmī, Mahārāja Parīkṣit used to imitate the worship of the family Deity by elderly members. Śrīla Viśvanātha Cakravartī also confirms the viewpoint of Jīva Gosvāmī. So accepting either of them, Mahārāja Parīkṣit was naturally inclined to Lord Kṛṣṇa from his very childhood. He might have imitated either of the above-mentioned activities, and all of them establish his great devotion from his very childhood, a symptom of a mahā-bhāgavata. Such mahā-bhāgavatas are called nitya-siddhas, or souls liberated from birth. But there are also others, who may not be liberated from birth but who develop a tendency for devotional service by association, and they are called sādhana-siddhas. There is no difference between the two in the ultimate issue, and so the conclusion is that everyone can become a sādhana-siddha, a devotee of the Lord, simply by association with the pure devotees. The concrete example is our great spiritual master Śrī Nārada Muni. In his previous life he was simply a boy of a maidservant, but through association with great devotees he became a devotee of the Lord of his own standard, unique in the history of devotional service.

From his very birth, Uddhava was a natural devotee of Lord Kṛṣṇa, or a nitya-siddha, a liberated soul.
(SB 3.2.2, Purport)

From his very birth, Uddhava was a natural devotee of Lord Kṛṣṇa, or a nitya-siddha, a liberated soul. From natural instinct he used to serve Lord Kṛṣṇa, even in his childhood. He used to play with dolls in the form of Kṛṣṇa, he would serve the dolls by dressing, feeding and worshiping them, and thus he was constantly absorbed in the play of transcendental realization. These are the signs of an eternally liberated soul. An eternally liberated soul is a devotee of the Lord who never forgets Him. Human life is meant for reviving one’s eternal relation with the Lord, and all religious injunctions are meant for awakening this dormant instinct of the living entity. The sooner this awakening is brought about, the quicker the mission of human life is fulfilled.

The nitya-siddha devotees never fall down to the region of the material atmosphere, even though they sometimes come onto the material plane to execute the mission of the Lord.
(SB 3.3.26, Purport)

Amongst the devotees of the Lord there are several divisions, mainly nitya-siddhas and sādhana-siddhas. The nitya-siddha devotees never fall down to the region of the material atmosphere, even though they sometimes come onto the material plane to execute the mission of the Lord. The sādhana-siddha devotees are chosen from the conditioned souls. Out of the sādhana devotees, there are mixed and pure devotees. The mixed devotees are sometimes enthusiastic about fruitive activities and are habituated to philosophical speculation. The pure devotees are free from all these mixtures and are completely absorbed in the service of the Lord, regardless of how and where they are situated. Pure devotees of the Lord are not enthusiastic to put aside their service to the Lord in order to go visit holy places of pilgrimage. A great devotee of the Lord in modern times, Śrī Narottama dāsa Ṭhākura, has sung like this: “To visit holy places of pilgrimage is another bewilderment of the mind because devotional service to the Lord at any place is the last word in spiritual perfection.”

Our relationship with Kṛṣṇa, the Supreme Personality of Godhead, is eternal. Nitya-siddha kṛṣṇa-prema. The pure souls are eternally in love with Kṛṣṇa.
(SB 7.7.39, Purport)

The entire world is described in Bhagavad-gītā as duḥkhālayam aśāśvatam (BG 8.15)—miserable and temporary. Economic development may be pleasing for some time, but it cannot endure. Thus many big businessmen are now very morose because they are being harassed by various plundering governments. In conclusion, why should one waste his time for so-called economic development, which is neither permanent nor pleasing to the soul? On the other hand, our relationship with Kṛṣṇa, the Supreme Personality of Godhead, is eternal. Nitya-siddha kṛṣṇa-prema. The pure souls are eternally in love with Kṛṣṇa, and this permanent love, either as a servant, a friend, a parent or a conjugal lover, is not at all difficult to revive. Especially in this age, the concession is that simply by chanting the Hare Kṛṣṇa mantra (harer nāma harer nāma harer nāmaiva kevalam (CC Adi 17.21)) one revives his original relationship with God and thus becomes so happy that he does not want anything material.

Sri Caitanya-caritamrta

The transference of the Lord from the heart of Jagannātha Miśra to the heart of Śacīmātā is explained by Śrīla Bhaktisiddhānta Sarasvatī Ṭhākura as follows: “It is to be concluded that Jagannātha Miśra and Śacīmātā are nitya-siddhas, ever-pure associates of the Lord.”
(CC Adi 13.86, Purport)

The transference of the Lord from the heart of Jagannātha Miśra to the heart of Śacīmātā is explained by Śrīla Bhaktisiddhānta Sarasvatī Ṭhākura as follows: “It is to be concluded that Jagannātha Miśra and Śacīmātā are nitya-siddhas, ever-pure associates of the Lord. Their hearts are always uncontaminated, and therefore they never forget the Supreme Personality of Godhead. A common man in this material world has a contaminated heart. He must therefore first purify his heart to come to the transcendental position. But Jagannātha Miśra and Śacīmātā were not a common man and woman with contaminated hearts. When the heart is uncontaminated, it is said to be in the existential position of Vasudeva. Vasudeva can beget Vāsudeva, or Kṛṣṇa, who is transcendentally situated.”

A nitya-siddha never forgets the service of the Lord. He is always engaged, even from childhood, in worshiping the Supreme Personality of Godhead.
(CC Madhya 3.167, Purport)

“The unsuccessful yogī, after many, many years of enjoyment on the planets of the pious living entities, is born into a family of righteous people, or into a family of rich aristocracy.” Mother Śacī, a nitya-siddha living entity, is an incarnation of mother Yaśodā. She appeared in the house of Nīlāmbara Cakravartī and was everlastingly engaged in the service of Lord Viṣṇu. Later she directly had as her child Lord Viṣṇu, Śrī Caitanya Mahāprabhu, and she served Him from the day of His appearance. This is the position of nitya-siddha associates. Śrī Narottama dāsa Ṭhākura therefore sings: gaurāṅgera saṅgi-gaṇe nitya-siddha kari māne. Every devotee should know that all the associates of Śrī Caitanya Mahāprabhu—His family members, friends and other associates—were all nitya-siddhas. A nitya-siddha never forgets the service of the Lord. He is always engaged, even from childhood, in worshiping the Supreme Personality of Godhead.

All nitya-siddhas within this material world may appear to toil like ordinary men, but they never forget their position as servants of the Lord.
(CC Madhya 5.113, Purport)

There are many devotees who are eternal servants of the Lord. They are specifically known as nitya-siddha, eternally perfect. Although the nitya-siddhas appear in the material world and seem to be common members of the world, they never forget the Supreme Personality of Godhead in any condition. This is the symptom of a nitya-siddha.

There are two kinds of living entities—nitya-siddha and nitya-baddha. The nitya-siddha never forgets his relationship with the Supreme Personality, whereas the nitya-baddha is always conditioned, even before the creation. He always forgets his relationship with the Supreme Personality of Godhead. Here the Lord informs the two brāhmaṇas that they are His servants birth after birth. The phrase birth after birth refers to the material world because in the spiritual world there is no birth, death, old age or disease. By the order of the Supreme Personality of Godhead, the nitya-siddha remains within this material world like an ordinary man, but the only business of the nitya-siddha is to broadcast the glories of the Lord. This incident appears to be an ordinary story about a marriage transaction involving two ordinary people. However, Kṛṣṇa accepted the two brāhmaṇas as His eternal servants. Both brāhmaṇas took much trouble in these negotiations, just like mundane people, yet they were acting as eternal servants of the Lord. All nitya-siddhas within this material world may appear to toil like ordinary men, but they never forget their position as servants of the Lord.

One who accepts the associates of Lord Caitanya Mahāprabhu as nitya-siddhas is certain to be elevated to the spiritual kingdom to become an associate of the Supreme Lord.
(CC Madhya 5.113, Purport)

The elderly brāhmaṇa belonged to an aristocratic family and was learned and wealthy. The young brāhmaṇa belonged to an ordinary family and was uneducated. But these mundane qualifications do not concern a nitya-siddha engaged in the service of the Lord. We have to accept the fact that the nitya-siddhas are completely distinct from the nitya-baddhas, who are ordinary human beings. Śrīla Narottama dāsa Ṭhākura confirms this statement:

One who accepts the associates of Lord Caitanya Mahāprabhu as nitya-siddhas is certain to be elevated to the spiritual kingdom to become an associate of the Supreme Lord. One should also know that Gauḍa-maṇḍala-bhūmi—those places in Bengal where Śrī Caitanya Mahāprabhu stayed—are equal to Vrajabhūmi, or Vṛndāvana. There is no difference between the inhabitants of Vṛndāvana and those of Gauḍa-maṇḍala-bhūmi, or Śrīdhāma Māyāpur.
One who is nitya-siddha has no business other than broadcasting the glories of the Lord all over the world according to his ability.
(CC Madhya 11.89, Purport)

A devotee is always thinking of how better to serve Lord Kṛṣṇa, the Supreme Personality of Godhead, and how to broadcast His name, fame and qualities throughout the world. One who is nitya-siddha has no business other than broadcasting the glories of the Lord all over the world according to his ability. Such people are already associates of Lord Caitanya Mahāprabhu. Therefore Narottama dāsa Ṭhākura says, nitya-siddha kari’ māne. One should not think that because Śrī Caitanya Mahāprabhu was personally present five hundred years ago, only His associates were liberated. Rather, Śrīla Narottama dāsa Ṭhākura says that anyone is a nitya-siddha if he acts on behalf of Śrī Caitanya Mahāprabhu by spreading the glories of the holy name of the Lord. We should respect those devotees preaching the glories of the Lord as nitya-siddha and should not consider them conditioned.

One who has transcended the material modes of nature is said to be on the Brahman platform. That is also the platform of nitya-siddha. The nitya-siddha not only stays on the Brahman platform but also works on that platform. Simply by accepting the associates of Lord Caitanya Mahāprabhu as nitya-siddha, one can very easily go back home, back to Godhead.

Nectar of Devotion

There are two classes of living entities—namely, nitya-siddha and nitya-baddha. The distinction is that the nitya-siddhas are eternally Kṛṣṇa conscious without any forgetfulness, whereas the nitya-baddhas, or eternally conditioned souls, are forgetful of their relationship with Kṛṣṇa.
(Nectar of Devotion 25)

Persons who have achieved eternal, blissful life exactly on the level of Śrī Kṛṣṇa, and who are able to attract Lord Kṛṣṇa by their transcendental loving service, are called eternally perfect. The technical name is nitya-siddha. There are two classes of living entities—namely, nitya-siddha and nitya-baddha. The distinction is that the nitya-siddhas are eternally Kṛṣṇa conscious without any forgetfulness, whereas the nitya-baddhas, or eternally conditioned souls, are forgetful of their relationship with Kṛṣṇa.

The position of the nitya-siddhas is explained in the Padma Purāṇa in connection with the narration of the Supreme Personality of Godhead and Satyabhāmā-devī. The Lord tells Satyabhāmā, “My dear Satyabhāmā-devī, I have descended to this earthly planet by the request of Lord Brahmā and other demigods. Those who are born into this family of Yadu are all My eternal associates. My dear wife, you should not consider that My associates are ever separated from Me; they are My personal expansions, and as such, you must know that they are almost as powerful as I am. Because of their transcendental qualities, they are very, very dear to Me, as I am very, very dear to them.” Anyone who becomes exhilarated by hearing of the pastimes of Lord Kṛṣṇa when He was present on this earth with His associates is to be understood as nitya-siddha, eternally perfect.